Roughly speaking, when \(\mathrm {Var}(\xi )<\infty \) , this estimate, with \(\sqrt{n\mathrm {Var}(\xi ^{(b_{n})})}\)  instead of \(v_{n}\) , follows from [1]} and when \(\mathrm {Var}(\xi )=\infty \)  this follows from [2]}. The identification of \(v_{n}\)  requires asymptotics estimates on the moments of \(\xi ^{(b_{n})}\) , which is the core of the proof of Theorem REF .
